Q. 14.2( 12 Votes )

The sum of the di

Answer :

Let ab be the 2-digit number.


Given that a + b = 11 and ab – ba = 9


In general, a 2-digit number ab made of digits a and b is equal in value to 10 × a + b = 10 a + b


Similarly, we have ba = 10 × b + a = 10b + b


From the problem statement, we know ab – ba = 9


(10a + b) – (10b + a) = 9


9a – 9b = 9


a – b = 1


So, we have a + b = 11 and a – b = 1. Adding these,


(a + b) + (a – b) = 11 + 1


2a = 12


a = 6


Using a – b = 1, we have b = a – 1


b = 6 – 1 = 5


So, ab = 65


Therefore, the number is 65.


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